Cournot Model

12 Key excerpts on "Cournot Model"

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  Microeconomics

  A Global Text

  • Judy Whitehead(Author)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  The game theory approach to modelling oligopoly in terms of competitors in a game with strategies and counter-strategies may be included among the traditional models. The models may be summarized as follows. Non-collusive models • The Cournot duopoly model • The Bertrand/Edgeworth duopoly model • The Chamberlin duopoly model. • The Sweezy Kinked Demand model. • The Stackleberg Solution model of ‘the sophisticated Duopolist’ 334 THE Cournot Model 12.2 Collusive models • Cartels • Price leadership • The low cost price leader • The dominant firm price leader • The barometric price leader Game theory The two-person, zero-sum, strictly determined game. Game theory provides an alternative way to model oligopoly in terms of strategy and counter-strategy. The two-person, zero-sum, strictly determined game is one of the simplest forms of the game that allows a clear insight into how the model works. These models are dealt with seriatim. 12.2 THE Cournot Model A study of the non-collusive models reveals that although the firms in the industry recognize their interdependence and this affects their behaviour, they do not resort to collusion. This, of course, tends to reduce firm and industry profits, reduce price and increase output. The Cournot Model is one of the earliest oligopoly models and, in its original form, is a duopoly model (two sellers). It is associated with the economist A. Cournot (1801–1877), who first presented the model in 1838, writing later in 1897. It is a costless production model related to sale of water from mineral springs. 12.2.1 Assumptions of the Cournot Model 1 The model is closed. There are two sellers of mineral water – each owns a mineral spring and no further entry takes place. 2 Both firms aim to maximize profit. 3 The firms have zero operating costs (hence TC = AC = MC = 0). Thus production is costless. 4 Firms sell in a market with a straight-line, negatively sloped demand curve.

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  Introduction to Game Theory in Business and Economics

  • Thomas J. Webster(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  We will begin our discussion with a graphical description of the Cournot Model . We will then reformulate the Cournot Model as a static, output-setting game involving continuous strategies. The Cournot Model is significant because it highlights the central role of strategic behavior in imperfectly competitive markets. F IGURE D8.1 Solution to Demonstration Problem 8.1 IMPERFECT COMPETITION 181 Cournot Model A static output-setting game in which firms in the same industry cannot subsequently switch strategies without great cost. In the Cournot Model, prices adjust to firms’ output decisions to clear the market. The Cournot Model is an output-setting game in which rival firms simultaneously determine their optimal output. An important assumption is that once output is determined, it cannot be changed, or at least not without significant economic cost. In the Cournot Model, output is the only decision variable. Once the firms’ output levels are determined, the market price adjusts to equate consumer demand with total industry supply. This functional relationship is summarized in Equation (8.1). P P Q dP Q dQ T T T = ( ) ( ) < ; 0 (8.1) where Q Q T i i n = = ∑ 1 (8.2) Our objective is to determine the Nash equilibrium output level for each firm in this one-time, static game in which player strategies are continuous. To simplify the analysis, we will assume that the industry comprises two profit-maximizing firms producing a homogeneous product. We will also assume linear market demand and constant marginal cost, which will be set equal to zero for diagrammatic convenience. These assumptions are depicted in Figure 8.3. We will analyze this static, output-setting game from firm A ’s perspective. To maximize profits, firm A will produce at an output level where MC = MR A . Since we have assumed that MC = 0, firm A will first consider producing at output level Q A at a price of P 1 . Since MC = 0, maximizing profits is equivalent to maximizing total revenue.

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  Industrial Organization

  Contemporary Theory and Empirical Applications

  • Lynne Pepall, Dan Richards, George Norman(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Augustin Cournot, a French mathematician, published his model in 1836. Although its insights remained largely unrecognized for the next 100 years, it is now at the foundation of models of oligopolistic markets. The story that Cournot told to motivate his analysis went as follows. Assume a single firm wishes to enter a market currently supplied by a monopoly. The entrant is able to offer a product that is identical in all respects to that of the incumbent monopolist and to produce it at the same unit cost. Entry is attractive because under the assumption of constant and identical costs, we know that the monopolist is producing where price is greater than marginal cost, which means that the price also exceeds the marginal cost of the would-be entrant. Hence, the entrant firm will see that it can profitably sell some amount in this market. However the new entrant will, Cournot reasoned, choose an output level that maximizes its profit, after taking account of the output being sold by the monopolist. Of course, if entry occurred and the new firm produced its chosen output, the monopolist would react. Before entry, the monopolist chose a profit-maximizing output assuming no other rivals. Now, the former monopolist will have to re-optimize and choose a new level. In so doing, the monopolist will (as did the new entrant previously) choose an output level that maximizes profits given the output sold by the new rival firm. This process of each firm choosing an output conditional on the other’s output choice is to be repeated—at least as a mental exercise. For every output choice by the incumbent, firm 1, the entrant, firm 2, is shown to have a unique, profit-maximizing response and vise-versa. Cournot called the graph representations of these responses Reaction Curves. Each firm has its own Reaction Curve that can be graphed in the q 1 q 2 quadrant.

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  Microeconomic Foundations II

  Imperfect Competition, Information, and Strategic Interaction

  • David M. Kreps(Author)
  • 2023(Publication Date)
  • Princeton University Press

    (Publisher)

  Chapter Eighteen Cournot and Bertrand Markets with a small number of sellers are quite common. Modeling the actions of those sellers—how they set prices and/or quantities, how they act and react to one another—has long challenged economists. Antoine Augustin Cournot, in 1838, and then Joseph Bertrand, in 1883, proposed simple equilibrium models in which the sellers act once, simultaneously and independently; models that come to very different (equilibrium) conclusions. These are early game-theoretic mod- els in economics—perhaps the earliest—appearing long before game theory was formalized. I doubt that there are many economic theorists today who view these two mod- els as realistic on their own. 1 However, they are often used as parts of theoretical models that explore important issues; Chapter 22 provides examples. And, because they are so simple, they are a good place to begin to develop models of imperfect competition. Moreover, modeled as games, they present the simplest sort of equi- librium: Nash equilibrium in strategic-form games, and so they get us started with game-theoretic methods. So in this (relatively short) chapter, we begin with the basic Cournot and Bertrand models and then look at some variations. 18.1. Basic Cournot Imagine that there are N suppliers of some perishable commodity. Because the good is a commodity, consumers are as happy with the product produced by one supplier as they are with product from any other. Because the good is perishable, it must be sold (and, presumably, consumed) within a short time following pro- duction. Imagine as well that production is done in distinct and remote locations, where each supplier n decides, on her own, an amount x n ≥ 0 to produce and 1 That said, I was privileged to attend a seminar at which Franklin Fisher presented to a room full of theorists his 1989 paper “Games economists play” (see the discussion in Chapter 17).

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  Industrial Organization

  Markets and Strategies

  • Paul Belleflamme, Martin Peitz(Authors)
  • 2015(Publication Date)
  • Cambridge University Press

    (Publisher)

  If there is a small number of big players that provide most of the industry output, then these firms may commit themselves to bring a certain amount of a product to the market. The market clearing may be performed by an auctioneer (who, for simplicity, is assumed not to charge for market transactions) who finds the highest price at which all offered units are sold. The resulting equilibrium allocation is then equivalent to the outcome in the quantity-setting game. We start our analysis of the Cournot Model with the simple case of an oligopoly facing linear demand for a homogeneous product and producing at constant marginal costs (Subsection 3.2.1 ). In order to gain further insight, we extend the initial setting by using general demand and cost functions (Subsection 3.2.2 ). 3.2.1 The linear Cournot Model We consider a homogeneous product market with n firms in which firm i sets q i . Total output is then q = q 1 + · · · + q n . The market price is given by the linear inverse demand P ( q ) = a − bq (with 3.2 Quantity competition 55 d ( q − i ) d ( q ′ − i ) q i a − bq − i a − bq ′ − i q ′ − i > q − i Price Figure 3.2 Residual demand for a Cournot oligopolist a , b > 0). Let us also suppose that the cost functions are linear: C i ( q i ) = c i q i (with 0 ≤ c i < a ∀ i = 1 , . . . , n ). We first solve the model in the most general case for any number of potentially heterogeneous firms ( c i = c j for any i = j ). We then use this general analysis in two specific cases: in a duopoly ( n = 2) and in a symmetric oligopoly ( c i = c ∀ i ). Cournot oligopoly with heterogeneous firms Let us denote by q − i ≡ q − q i the sum of the quantities produced by all firms but firm i . The inverse demand can then be rewritten as P ( q ) = ( a − bq − i ) − bq i ≡ d i ( q i ; q − i ) .

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  Microeconomics

  • David Besanko, Ronald Braeutigam(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  These beliefs might make sense in a market such as the U.S. airline industry in the early 2000s, which had significant excess capac- ity. Many airlines at that time believed that they would fly their planes virtually empty unless they cut their prices below their competitors. (Of course, if all firms in the mar- ket think this way, each one will attempt to steal business from its competitors through price cutting, with the result that prices drop to marginal cost.) 15 The idea that the Cournot equilibrium can (under some circumstances) emerge as the outcome of a “two-stage game” in which firms first choose capacities and then choose prices is due to D. Kreps and J. Scheinkman, “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes,” Bell Journal of Economics 14 (1983): 326–337. CHAPTER 13 MARKET STRUCTURE AND COMPETITION 574 THE STACKELBERG MODEL OF OLIGOPOLY In the Cournot Model of quantity setting, both firms are assumed to choose their quantities simultaneously. However, in some situations, it might be more natural to assume that one firm chooses its quantity before the other firms make their choices. This assumption may be especially natural if we think of the quantities as levels of pro- duction capacity. In many oligopolistic industries, capacity expansion decisions tend to occur sequentially rather than simultaneously. For example, in the U.S. turbine gen- erator industry of the 1950s and 1960s, Westinghouse and Allis-Chalmers generally undertook major capacity expansions only after industry leader, General Electric, had expanded its capacity. 16 The Stackelberg model of oligopoly pertains to a situation in which one firm acts as a quantity leader, choosing its quantity first, with all other firms acting as fol- lowers, making their quantity decisions after the leader has moved.

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  Microeconomics

  Theory and Applications

  • Edgar K. Browning, Mark A. Zupan(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  When Artesia sees Utopia producing 32 units, and decides on 32 for itself, based on the assumption that Utopia will not change its output, it will be right. The assumption becomes implausible only for adjustments to the equilibrium. Second, the assumption is more plausible the larger the number of firms in the market. (The Cournot Model can readily accommodate any number of firms greater than two, and, in general, the greater the number of firms, the larger the total industry output as a percentage of the competitive output.) With 10 equal-sized firms, if one changes its output by, say, 10 percent, it will represent only a one percent change in industry output, which will have a small effect on price. The other firms may not associate such a small price change with the actions of one firm because other things, like shifting market demand, can also affect price. Other Oligopoly Models The Cournot Model serves as a good introduction to oligopoly models by highlighting the importance of how firms handle the mutual interdependence in such markets. In this sec- tion we explore two other models of oligopoly. Although they by no means represent all the models that have been suggested, they do indicate some different assumptions a firm in an oligopoly market might make about rival firms’ actions. The Stackelberg Model Recall that in the Cournot Model, each firm takes other firms’ outputs as constant in deter- mining its own output. We saw, however, that this assumption may not be valid. So now sup- pose that in the same two-firm example, we have one firm that continues to behave in the naive Cournot fashion, while the other firm wises up and realizes that it should not assume its rival’s output doesn’t change. In fact, let’s assume that Artesia realizes how Utopia chooses its output (from its reaction curve) and see whether Artesia can use that information to realize greater profit.

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  Essays in Mathematical Economics, in Honor of Oskar Morgenstern

  • Martin Shubik(Author)
  • 2015(Publication Date)
  • Princeton University Press

    (Publisher)

  PART V Management Science CHAPTER 19 Some Notes on Oligopoly Theory and Experiments By DAVID H. STERN* The market situation in which a small number of sellers (two or more) are competing with each other in selling to a public consisting of many buyers is called oligopoly. In the three sections of this paper we analyze the structure of a certain class of oligopoly markets, catalog several of the hypotheses that have been suggested for the behavior of firms in such markets, and describe the procedure and results of several laboratory experiments aimed at providing evidence concerning the truth of these hypotheses. The first attempt to analyze oligopoly markets was made by Augustin Cournot in 1838; 1 in this paper we will be concerned with a market model only slightly more general than his. Our model involves five kinds of variables: number of business firms; market price; and, for each firm, quantities produced, unit cost of production, and profits. Other variables, such as advertising, investment in plant and equipment, market power, re- search and development, and personality differences between business- men, are covered by a general ceteris paribus assumption. Of the included variables, only the quantities produced by each firm are decision variables; hence we call our model the Cournot quantity oligopoly model. 2 The symbols we will need to specify this model are: η Number of sellers. qi (i = 1,. . ., n) Quantity of product produced and supplied to the market by „ seller /. Q = Σ ΐ i Total quantity of product pro- t=1 duced and supplied to the market by all sellers. * Unaffiliated, residing in San Diego, California. This work was supported partly by the Office of Naval Research under Task 047-003 (Management Sciences Research Project), and partly by the Western Management Science Institute under a grant from the Ford Foundation. Reproduction in whole or in part is permitted for any purpose of the United States Government.

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  Contemporary Industrial Organization

  A Quantitative Approach

  • Lynne Pepall, Dan Richards, George Norman(Authors)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  In addition, high cost firms can survive in a Cournot Model of competition—although they will be less profitable than lower-cost rivals. This is not possible in the basic Bertrand model of 168 Oligopoly and Strategic Interaction price competition with identical products. In that case, only the lowest-cost producers can survive market competition. However, the efficient outcome predicted by the simple Bertrand model depends upon two key assumptions. The first is that firms have extensive capacity so that it is possible to serve all a rival’s customers after undercutting the rival’s price. The second key assumption is that the firms produce identical products so that relative price is all that matters to consumers when choosing between brands. If either of these assumptions is relaxed, the efficiency outcome of the simple Bertrand model no longer obtains. If firms must choose production capacities in advance, the outcome with Bertrand price competition becomes closer to what occurs in the Cournot Model. If products are differentiated, prices are again likely to remain above marginal cost, and given the fierceness of price competition, firms have a real incentive to differentiate their products. One approach to modeling product differentiation is the Hotelling (1929) spatial model, which we first introduced in Chapter 3. This model uses geographic location as a metaphor for differences between versions of the same product. It thereby makes it possible to consider price competition between firms selling differentiated products. The Hotelling model makes it clear that Bertrand competition with differentiated products does not result in efficient marginal cost pricing. It also makes clear that the deviation from such pricing depends on how much consumers value variety among products. The greater value that the typical consumer places on getting her most preferred version of the product, the higher prices will rise above marginal cost.

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  Managerial Economics

  A Strategic Approach

  • Robert Waschik, Tim Fisher, David Prentice(Authors)
  • 2010(Publication Date)
  • Routledge

    (Publisher)

  Before we describe the outcome of quantity competition, it is appropriate to describe some examples of what we mean by quantity competition. In general, quantity competition can cover a considerable number of market situations, where a manager can choose from a broad set of choice variables. In the simplest case, a firm which competes in a market with quantity competition must choose the quantity of output to maximize profits, be it a farmer deciding upon the number of hectares of wheat to plant or an oil-producing firm deciding on the number of barrels of oil to extract. Alternatively, quantity competition can refer to the problem where a manager must decide upon the capacity of a new plant. Should the firm invest in capacity to be able to potentially supply the entire market, or is it best to limit capacity to effectively supply only a limited and well-defined market segment?

  Instead, we could think of quantity competition as representing competition over the type of good to be produced. Should the firm design and sell a very high-quality good, or will the firm be better off mass-producing a relatively low-quality product?

  We will see that our simple model of quantity competition can be adapted to describe many varied types of competition, and in later chapters, we will examine a number of special cases. For now, we will describe the basic model of quantity competition or Cournot competition .1 Suppose we consider a market consisting of two firms producing an identical commodity like wheat or oil. The structure of demand for this commodity is summarized by the inverse demand function

  p = P (q 1 + q 2 ),

  where q 1 is the quantity of the commodity q sold by firm 1, and q 2 the quantity sold by firm 2. The structure of competition between these two firms can be summarized by the following assumptions:

  • The model is inherently static in nature, so that both firms choose outputs at the same time. • All firms have full information about market demand, about their own costs of production, and about the structure of the other firms’ costs. • There is neither entry of new firms nor exit of existing firms. • Consumers incur no transport costs in buying from either firm 1 or firm 2, so a consumer will always buy from the firm selling at the lowest price.

  Let’s look at each of these assumptions in turn, since they are very important in defining the outcome of competition in this market. To begin with, the model is static. Both firms will choose quantities q 1 and q 2 at the same time. This means that neither firm has the ability to go first and commit to a strategy before the other firm. Of course, it may be important to include some sort of dynamic element to the model, if it is important to represent the fact that one firm can choose a strategy before the other. But this would be a model which is fundamentally different from the Cournot Model, and as such is described in Section 6.3

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  Agents, Games, and Evolution

  Strategies at Work and Play

  • Steven Orla Kimbrough(Author)
  • 2011(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  Permission from Springer to republish this material is gratefully acknowledged. Chapter 11 Oligopoly: Bertrand Competition 11.1 Price Competition The Bertrand model models competition on the basis of price in an oligopoly. Each firm privately proposes a unit price for the goods on order and the lowest-price bid wins all of the business. What will the market price be? If there are very many firms in the market, it is easy to believe that the competitive price will prevail. The Bertrand model teaches us that this is also true in even the smallest oligopoly, consisting of just two firms. Here is a standard summary of the reasoning from a standard microeconomics text. If firm 1 really believes that firm 2 will charge a price ˆ p that is greater than the marginal cost, it will always pay firm 1 to cut its price to ˆ p − ε . But firm 2 can reason the same way! Thus any price higher than marginal cost cannot be an equilibrium; the only equilibrium is the competitive equilibrium. [322, page 488] In a different text (still standard) the same author makes the following remarks on the Bertrand result. It may seem somewhat paradoxical that we get price equal to marginal cost in a two-firm industry. Part of the problem is that the Bertrand game is a one-shot game: players choose their prices and then the game ends. This is typically not a standard practice in real-life markets. One way to think about the Bertrand model is that it is a model of competitive bidding. Each firm submits a sealed bid stating the price at which it will serve all customers; the bids are opened and the lowest bidder gets the customers. Viewed this way, the Bertrand result is not so paradoxical. [321, 293] Whether the one-shot result is paradoxical or not, we are interested in the iterated game, which is not addressed by the Bertrand model. The iterated game of price competition in an oligopoly is the subject of this chapter. 243

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  Handbook of Law and Economics

  • A. Mitchell Polinsky, Steven Shavell(Authors)
  • 2007(Publication Date)
  • North Holland

    (Publisher)

  4.1 Oligopoly theory and unilateral competitive effects

  The basic idea underlying theories of unilateral effects is that the merged firm will have an incentive to raise its price(s), in comparison with the pre-merger price(s), because of the elimination of direct competition between the two firms that have merged. The examination of specific oligopoly models makes it possible to quantify the effects, which is important for merger enforcement. First, quantification can help to identify the mergers that are most likely to have significant price effects and thus cause significant harm to consumers. These are the mergers that presumably warrant further scrutiny, if not prohibition. Second, quantification allows us to estimate the merger efficiencies necessary to offset the loss of competition and thereby allow the merger to pass muster according to the consumer surplus or total welfare standard.

  4.1.1 Cournot Model with homogeneous products

  We begin by studying the effects of mergers in the Cournot oligopoly model described in subsection 2.3.1 . The Cournot Model seems like a good starting place since it generates a number of sensible predictions relating market structure to the equilibrium outcome. In particular, we derived equation (3) that relates a firm’s price-cost margin to its market share and the market elasticity of demand. In the special case with constant and equal marginal costs, each firm has a market share of , and the Cournot Model predicts that the margin of each firm will be given by . We also derived an expression for the industry-wide average, output-weighted, price-cost margin, that is, , namely expression (4) : , where, recall, is the Herfindahl-Hirschman Index (HHI) of market concentration.

  The idea that a firm with a large share will have more market power, and thus will charge a higher price (but still less than the monopoly price) has been very influential in horizontal merger enforcement. So has the idea that margins are higher in more concentrated industries. In fact, based partially on the expression for the PCM, the Merger Guidelines measure market concentration using the HHI. At the same time, it is recognized that the margins of all firms in a given market are lower if the elasticity of demand in that market as a whole is large, a subject to which we will return in discussing market definition in subsection 4.5

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